(a) You are trying to develop a strategy for investing in two different stocks, Stock A and Stock B. The anticipated annual return for a $1000 investment in each stock under four different conditions has the following probability distribution:
condition StockA Stock B
0.1 Recession -$50 -$120
0.4 Slow growth $20 $0
0.4 Moderate growth $80 $140
0.1 Fast growth $150 $250
Compute the portfolio expected return and portfolio risk if the percentage invested in Stock A is either 30%, 50% or 70%. On the basis of these results, which portfolio would you recommend? Briefly explain the reason for your answer.
b) In a triangle taste test conducted at a Woolworths supermarket, the taster is presented withthree samples, two of which are alike, and is asked to pick the odd one by tasting. If a tasterhas no well-developed sense of taste and picks the odd one by guessing,
(i) What is the probability that in six trials (ie. six taste tests) he or she will make at least one correct decision.
(ii) How many correct decisions would you expect in six trials (ie. six taste tests).
(c) A manufacturing plant's main production line breaks down an average of 2.4 times per day.
Assume breakdowns occur randomly.
(i) What is the probability of at least 3 breakdowns in a day.
(ii) How many breakdowns would you expect in seven days.